Capacity and principal eigenvalues: the method of enlargement of obstacles revisited
Capacity and principal eigenvalues: the method of enlargement of obstacles revisited
We describe a coarse graining method, which provides lower bounds on the principal Dirichlet eigenvalue of the Laplacian in regions receiving small obstacles, and sharpens the previous method of enlargement of obstacles. Based on a quantitative Wiener criterion, one replaces the actual obstacles by obstacles of a much larger size. …